London has been battered by 50mph winds that have felled trees and caused travel chaos. Powerful gusts swept across the capital as the Met Office issued a yellow "be aware" weather alert for most of the country.

If ever a piece of theatre worked magic then it must be War Horse. Nick Stafford’s persuasive adaptation of Michael Morpurgo’s children’s novel, premiered at the National in 2007, now canters into town with the confidence of a natural-born winner in this superbly integrated production by Marianne Elliott and Tom Morris. It should appeal to imaginations aged anything from 12 to 92.

The key to the show’s almost eerie success is its creation of larger-than-horse-life equines — the puppet-contraptions, Joey and Topthorn. As conceived with startling brilliance by Basil Jones and Adrian Kohler and fashioned from wood leather, string and canvas, each puppet horse requires three puppeteers to operate it. Director of Horse Choreography Toby Sedgwick makes these imitation-animals amazing. Somehow you forget the existence of the puppeteers, even as they bring these creatures to life. It is as if they were anthropomorphous: we identify with them.

War Horse, though, is not a tear-inducing tribute to animals cruelly caught up in our wars. Something more serious and interesting is afoot.

Initially set in a Devon village in summer 1914, Stafford depicts an impoverished farming family — beset by Anglo-Saxon froideur and emotional reserve. The violent paterfamilias is at loggerheads with his son (Kit Harrington’s withdrawn Albert). This teenager’s passion for Joey is quintessentially English.

Love for an animal substitutes for human love. So Albert coaxes the horse into ploughing to save him from being sold, suffers agonies when the animal is requisitioned for war and is improbably reunited with Joey when he goes to war himself.

Rae Smith’s rear-stage projection screen, with sketch-book drawings of rural England, is soon rendered dramatic with Vorticist Images of the Western Front. Those Puppet horses thunder across stage in a cavalry charge, which leaves one of them writhing in agony; a gun-carriage lumbers across no-man’s land; Joey whinnies trapped in barbed wire.

The second half, when the horse falls into enemy hands and the air is full of actors speaking English in German and French accents, loses narrative drive. Even so War Horse proves a rare winner.